Harmonic basis functions for spatial coding in the cat striate cortex

The number of subregions in the activity profiles of simple cells varies in different cells from 2-8; that is, the number of cycles in the weighting function varies from 1-4. The distribution of receptive-field (RF) sizes at eccentricities of 0-6 deg are clustered at half-octave intervals and form a discrete distribution with maxima at 0.62, 0.9, 1.24, 1.8, 2.48, and 3.4 deg. The spatial frequencies to which the cells are tuned are also clustered at half-octave intervals, forming a discrete distribution peaking at 0.45, 0.69, 0.9, 1.35, 1.88, 2.7, 3.8, and 5.6 cycles/deg. If we divide the RF sizes by the size of the period of the subregions, then the average indices of complexity (really existing) or the number of cycles in the weighting function form (after normalization) the sequences: 1, 1.41, 2.0, 2.9, 4.15. The relation between the bandwidth of the spatial-frequency characteristic and the optimal spatial frequency is in accordance with predictions of the Fourier hypothesis. The absolute bandwidth does not change with the number of cycles/module. This means that inside the module the absolute bandwidth does not change with the number of the harmonic. The results allow us to suggest the following. A module of the striate cortex, which is a group of cells with RFs of equal size projected onto the same area of central visual field, accounts for the Fourier description of the image. The basis functions of the module are composed of four harmonics only, irrespective of size and position of the module. Besides linear cells (sinusoidal and cosinusoidal elements), the module contains nonlinear cells, performing a nonlinear summation of the responses of sinusoidal and cosinusoidal elements. Such cells are characterized by an index of complexity which is more than the number of cycles in the weighting function and by marked overlap of ON and OFF zones. The analysis of organization suggests that the cells can measure the amplitude and phase of the stimulus.